Volumetric Topological Analysis: A Novel Approach for Trabecular Bone Classification on the Continuum Between Plates and Rods

Trabecular bone (TB) is a complex quasi-random network of interconnected plates and rods. TB constantly remodels to adapt to the stresses to which it is subjected (Wolff's Law). In osteoporosis, this dynamic equilibrium between bone formation and resorption is perturbed, leading to bone loss and structural deterioration. Both bone loss and structural deterioration increase fracture risk. Bone's mechanical behavior can only be partially explained by variations in bone mineral density, which led to the notion of bone structural quality. Previously, we developed digital topological analysis (DTA) which classifies plates, rods, profiles, edges, and junctions in a TB skeletal representation. Although the method has become quite popular, a major limitation of DTA is that it provides only hard classifications of different topological entities, failing to distinguish between narrow and wide plates. Here, we present a new method called volumetric topological analysis (VTA) for regional quantification of TB topology. At each TB location, the method uniquely classifies its topology on the continuum between perfect plates and perfect rods, facilitating early detections of TB alterations from plates to rods according to the known etiology of osteoporotic bone loss. Several new ideas, including manifold distance transform, manifold scale, and feature propagation have been introduced here and combined with existing DTA and distance transform methods, leading to the new VTA technology. This method has been applied to multidetector computed tomography (CT) and micro-computed tomography (
$\mu{\hbox {CT}}$
) images of four cadaveric distal tibia and five distal radius specimens. Both intra- and inter-modality reproducibility of the method has been examined using repeat CT and
$\mu{\hbox {CT}}$
scans of distal tibia specimens. Also, the method's ability to predict experimental biomechanical properties of TB via CT imaging under in vivo conditions has been quantitatively examined and the results found are very encouraging.